TY - JOUR

T1 - A canonical construction for nonnegative integral matrices with given line sums

AU - Fernandes, Maria do Rosário Silva Franco

AU - F. da Cruz, Henrique

N1 - Foundation for Science and Technology (UID/MAT/00212/2013)

PY - 2015

Y1 - 2015

N2 - Let p be a positive integer and let A((p)) (R, S) be the class of nonnegative integral matrices with entries less than or equal to p, with row-sum partition R, and column-sum partition S. In this paper we state a new necessary and sufficient condition for A((p)) (R, S) not equal empty set. This condition generalizes the well known Gale-Ryser theorem. We also present a canonical construction for matrices in A((p)) (R, S).

AB - Let p be a positive integer and let A((p)) (R, S) be the class of nonnegative integral matrices with entries less than or equal to p, with row-sum partition R, and column-sum partition S. In this paper we state a new necessary and sufficient condition for A((p)) (R, S) not equal empty set. This condition generalizes the well known Gale-Ryser theorem. We also present a canonical construction for matrices in A((p)) (R, S).

KW - Algorithm

KW - Integral matrices with given lines

KW - Partition domination

U2 - 10.1016/j.laa.2015.06.033

DO - 10.1016/j.laa.2015.06.033

M3 - Article

SN - 0024-3795

VL - 484

SP - 304

EP - 321

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -